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What is the limit of #cos(x-9)/sqrt(x-3)# as #x# approaches to 9?

Answer 1

#1/sqrt(6)#

Since the function is defined at #x = 9#, we can simply evaluate it at #x=9# to obtain the limit, evaluating, we get #cos(0)/sqrt(6) = 1/sqrt(6)#

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Answer 2

Evelyn Agard

The limit of ( \frac{\cos(x-9)}{\sqrt{x-3}} ) as ( x ) approaches 9 is ( \frac{1}{\sqrt{6}} ), or approximately 0.408.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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